Abstract

We consider the enveloping semigroup of a flow generated by the
action of a semitopological semigroup on any of its semigroup
compactifications and explore the possibility
of its being one of the known semigroup compactifications again.
In this way, we introduce the notion of E-algebra, and show that
this notion is closely related to the reductivity of the semigroup
compactification involved. Moreover, the structure of
the universal Eℱ-compactification is also given.

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